6. Prove: (1-cotA)² + (tanA-1)² = 4cosec²2A-4Cosec2A​

The probability that at most 13 of the residers in the sample entered a jury process in the once 12 months is 0.000158.

A normal distribution, also known as a Gaussian distribution or bell wind, is a probability distribution that's symmetric and bell- shaped. It's characterized by its mean( μ) and standard divagation( σ).

Given

Sample size( n) = 500

Probability of an individual entering a jury process( p) = 15 = 0.15

We want to calculate the probability that at most 13 of the residers in the sample entered a jury process.

Let X be the arbitrary variable representing the number of residers who entered a jury process in the sample.

Using the binomial accretive distribution function( CDF), we can calculate the probability as follows

P( X ≤ 13 of n) = Σ( k = 0 to k = 0.13 n)( n C k)

Here, n = 500

p = 0.15

k = int(0.13 n)

So, binom.cdf( int(0.13 500), 500,0.15) ≈0.000158

Thus, The likelihood that 13% of the sample's residents received a jury summons in the previous year is 0.000158.

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The question attached here is seems to be incomplete, the complete question is

What proportion of US Residents receive a jury summons each year? A polling organization plans to survey a random sample of 500 US Residents to find out. Let be the proportion of residents in the sample who received a jury summons in the previous 12 months. According to the National Center for State Courts, 15 \% of US residents receive a jury summons each year. Suppose that this claim is true.

5. Calculate the probability that at most 13% of the residents in the sample received a jury summons in the past 12 months.

Answer:

Glad we helped

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

We Know

30% of r = 33

Find 1% by taking

33 / 30 = 1.1

What is 70% of R?

We take

1.1 x 70 = 77

So, 70% of R is 77

The question requires to first find the value of R by solving the equation (0.30*R = 33). Then, calculate 70% of R by multiplying the found R value with 0.70.

The question tells us that 30% of R equals 33. To find the value of R, we can set up an equation where 0.30 (which is 30% in decimal form) times R equals 33. Dividing both sides of the equation by 0.30 will give us the value for R. Once we have found R, we can then find 70% of R by multiplying R by 0.70 (70% in decimal form).

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Answer:

a) 675

b) 12

c) y = 12x + 675

d) y = 12 (500) + 675 = $6,675

The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( [tex]e^{(-λ)[/tex] * [tex]λ^k[/tex]) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = ([tex]e^{(-72.8)[/tex]* [tex]72.8^(70)[/tex]) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

[tex]Z = (X - mean) / \sqrt{(variance)[/tex]

Fοr X = 70, we have:

Z = (70 - 1.4) / [tex]\sqrt{(1.4)[/tex] ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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The value of M - N is [tex]8x^2[/tex] + 11x - 9 by subtracting the value of N from the value of M.

To find the value of M - N, we first need to subtract the second polynomial N from the first polynomial M.

M - N = ([tex]5x^2[/tex] + 7x - 4) - ([tex]-3x^2[/tex] - 4x + 5)

To subtract the polynomials, we need to add the opposite of the second polynomial (i.e., add the negative of N) to the first polynomial M:

M - N = [tex]5x^2[/tex] + 7x - 4 + [tex]3x^2[/tex] + 4x - 5

Now we can combine like terms:

M - N = ([tex]5x^2 + 3x^2[/tex]) + (7x + 4x) + (-4 - 5)

M - N = [tex]8x^2[/tex] + 11x - 9

Therefore, the value of M - N is [tex]8x^2[/tex] + 11x - 9.

In summary, we found the value of M - N by subtracting the polynomial N from the polynomial M and then combining like terms. The resulting polynomial is [tex]8x^2[/tex] + 11x - 9.

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Answer:

  428.75π ft³

Step-by-step explanation:

You want the exact volume of a cylinder 35 ft high with a radius of 3.5 ft.

The volume is given by the formula ...

  V = πr²h

  V = π(3.5 ft)²(35 ft) = 428.75π ft³ . . . . . use the given values

The exact volume of the cylinder is 428.75π ft³.

Answer:

C

Step-by-step explanation:

(a) We can rewrite 32 as 2^5, so we have:

8^(2x) = (2^5)^(x+3)

Simplifying the right side, we get:

8^(2x) = 2^(5x+15)

(b) Now we can use the fact that 8 is 2^3, so we can rewrite the left side as (2^3)^(2x) = 2^(6x), giving us:

2^(6x) = 2^(5x+15)

Since the bases are equal, we can equate the exponents and solve for x:

6x = 5x + 15

x = 15

Therefore, the solution is x = 15.

The value of x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.

We know that Figure A is a scaled image of Figure B, with a scale of 1:7. This means that every length in Figure A is one-seventh the length of the corresponding length in Figure B. For example, if a side in Figure B is 14 units long, the corresponding side in Figure A would be 2 units long (14 divided by 7).

In question a side on figure A is 3 units:

Side on Figure B = 7 * Side on Figure A

x = 7 * 3

x = 21 units

Therefore, x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.

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The complete question is :

Figure A is a scale image of Figure B, as shown.

The scale that maps Figure A onto Figure B is 1:7

Enter the value of x.

The missing value that completes the frequency table is 100.

A frequency table is a statistical tool that summarizes data by displaying the frequency (or count) of each category or interval in a data set. It is commonly used in data analysis to organize and understand categorical or numerical data.

The missing value is the frequency for the value range between 28 and 30 (i.e 28 ≤ x ≤30). Looking at the histogram, you will notice that the frequency for the value between 28 and 30 is 100 (Check the attached image).

Therefore, the missing value is 100.

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Answer: 2sw or 2ab

Step-by-step explanation:

Answer:

Step-by-step explanation: We know that ,

Area of circle =πr² and

r = radius of circle.

Now,

Diameter of circle =56 cm [given]

So, radius of circle=D/2=56/2

Radius of circle=28

Now,

Area of circle=πr²

Area of circle=22/7 ×(28)² [π=22/7]

Area of circle=22×4×28

Area of circle=2464cm²

Hence, Area of circle is 2464cm²

I hope it's help you.

Answer:

48 cm²

Step-by-step explanation:

Area of circle formula:  A = πr²

                                          = π (d/2)²

                                          = 3.14 * (4)²

                                          = 50.24

The area of the circle is closest to Option D, 48 cm²

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=\textit{elapsed time} \end{cases} \\\\\\ A = 50(1 + 0.2)^{t} \implies \boxed{A =50(1.2)^t}[/tex]

Answer: 37

Step-by-step explanation: so first you have to realize that i what I’m doing and you not listen to me

By using the cosines law we can say that, Velma and Fred are approximately 17.39 meters apart.

What is law of cosine?

The Law of Cosines is a formula used in trigonometry to relate the sides and angles of a triangle. It states that for any triangle with sides a, b, and c and angles A, B, and C opposite those sides, the following equation holds:

[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]

where c is the side opposite angle C.

We can solve this problem using the law of cosines. Let's call the distance between Velma and Fred "[tex]$d$[/tex]". Then, we have:

[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]

where [tex]$c$[/tex] is the distance between Velma and Fred (which we want to find), [tex]$a$[/tex] is the distance between Shaggy and Velma (which is 20 meters), [tex]$b$[/tex] is the distance between Shaggy and Fred, and [tex]$C$[/tex] is the angle formed at Shaggy (which is 30 degrees).

We can rearrange this equation to solve for [tex]$d$[/tex]:

[tex]$d^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]

[tex]$d^2 = 20^2 + b^2 - 2(20)(b) \cos(30)$[/tex]

[tex]$d^2 = 400 + b^2 - 20b \sqrt{3}$[/tex]

We also know that the angle formed at Fred is 105 degrees, which means that the angle formed at Velma is 45 degrees (since the angles in a triangle sum to 180 degrees). This means that we can use the law of sines to find the value of [tex]$b$[/tex]:

[tex]$\dfrac{b}{\sin(B)} = \dfrac{a}{\sin(A)}$[/tex]

[tex]$\dfrac{b}{\sin(105)} = \dfrac{20}{\sin(45)}$[/tex]

[tex]$b = 20 \dfrac{\sin(105)}{\sin(45)}$[/tex]

[tex]$b \approx 27.68$[/tex]

Now we can substitute this value of [tex]$b$[/tex] into the equation we derived earlier to find [tex]$d$[/tex]:

[tex]$d^2 = 400 + (27.68)^2 - 20(27.68)\sqrt{3}$[/tex]

[tex]$d \approx 17.39$[/tex]

Therefore, Velma and Fred are approximately 17.39 meters apart.

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Answer: it slithers

Step-by-step explanation:

To further explain it They move by dragging their body throughout in the form of loops. Hence, snakes have a crawling or slithering type of movement

Answer:

Overlapping belly scales provide friction with the ground that gives snakes a preferred direction of motion, like the motion of wheels or ice skates.

Step-by-step explanation:

Hope this helps! =D

Mark me brinaliest!=D

Therefore, the value of x in each triangle is approximately 5.4 and 11.1, respectively.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, which are used to relate the angles of a triangle to the lengths of its sides. Trigonometry has a wide range of applications in fields such as physics, engineering, navigation, surveying, and astronomy. For example, trigonometry is used in navigation to calculate the angles between a ship and a lighthouse, or between two ships, in order to determine their relative positions. In engineering, trigonometry is used to calculate the forces acting on structures such as bridges and buildings, and to design and build machines that rely on the principles of motion and energy.

Here,

For the first triangle, we have:

Using the sine ratio,

sin(36) = x / 9

Solving for x, we get:

x = 9 sin(36)

≈ 5.4

Rounding to the nearest tenth, we get:

x ≈ 5.4

For the second triangle, we have:

Using the tangent ratio,

tan(27) = x / 21

Solving for x, we get:

x = 21 tan(27)

≈ 11.1

Rounding to the nearest tenth, we get:

x ≈ 11.1

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To choose a simple random sample assign different numbers to the house and visit by choosing randomly.

To choose a simple random sample of the 3 homes to survey,

Jerome could assign each home a number from 1 to 10,

And then use a random number generator or a table of random numbers to select three numbers.

He would then visit the homes corresponding to those numbers for the survey.

For example,

if he assigned the following numbers to each home,

1, 2, 3, 4, 5, 6, 7, 8, 9 ,10

He could use a random number generator or table of random numbers to select three numbers, such as 2, 5, and 9.

He would then visit the homes at 2, 5, 9 for the survey.

If someone is not home when Jerome visits,

He should make a note of it and try to arrange a time to come back and conduct the survey.

If it is not possible to arrange another time,

He should make a note that the household was not surveyed and move on to the next household in the sample.

It is important to keep track of which households were surveyed and which were not.

And to try to minimize any biases that may arise from nonresponse.

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By answering the presented question, we may conclude that height of the cone is approximately 2.9 centimeters.

A cone is a three-dimensional geometric shape having a flat base and a smooth tapering apex, also known as a vertex. A cone is formed on a plane with no vertices by joining a sequence of line segments, half-lines, or lines that are common to all points on the base. A cone is a three-dimensional structure with a smooth transition from a flat, usually circular, base to the vertex or apex, which acts as the axis to the centre of the base. A cone is a three-dimensional geometric form having an upwardly flattened curving surface.

volume of a cone:

[tex]V = 1/3 * \pi * r^2 * h\\r = 4 cm\\V = 143.6 cm^3\\143.6 = 1/3 * \pi * 4^2 * h\\143.6 = 16/3 * \pi * h\\h = 143.6 / (16/3 * \pi)\\h = 2.9 cm\\[/tex]

height of the cone is approximately 2.9 centimeters.

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Answer:

Step-by-step explanation:
[tex]168yd^{2}[/tex]

Answer:

168 yd²

Step-by-step explanation:

4 × 7 yd × 12 yd / 2 = 168 yd²

a) The time that Rodrigo spent practicing during the third week is 5.42 hours.

b) The equation that represents the problem is 15¹/₃ = 5¹/₄ + 4²/₃ + x.

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions are equal or equivalent.

Equations are represented using the equal symbol (=), unlike algebraic expressions that contain variables, constants, numbers, and values.

The time spent during the first week = 5¹/₄ hours

The time spent during the second week = 4²/₃ hours

The total time spent during the three weeks period = 15¹/₃ hours

Let the time spent during the third week = x

15¹/₃ = 5¹/₄ + 4²/₃ + x

x = 15¹/₃ - (5¹/₄ + 4²/₃)

x = 5.41663

Thus, solving the equation, Rodrigo spent 5.42 hours practicing the guitar during the third week.

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Answer:

8.

Step-by-step explanation:

That would be by a factor of 2^3 = 8.

Answer:

Step-by-step explanation:

The local minimum value of a graph is the point where the graph changes from a decreasing function to an increasing function.

The probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

To find the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday, we need to multiply the probabilities of these two events occurring.

The probability of selecting a gold short sleeve top on Monday is 2/6, or 1/3. There are 2 gold short sleeve tops out of a total of 6 uniforms.

After selecting a gold short sleeve top on Monday and not replacing it, there are 5 uniforms left, of which 2 are red short sleeve tanks. Therefore, the probability of selecting a red short sleeve tank on Tuesday is 2/5.

To find the probability of both events occurring, we multiply the probabilities together:

(1/3) * (2/5) = 2/15

Therefore, the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

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The function g(x)=3^x change over the interval from x=8 to x=10 by a factor of 9

The function g(x)=3^x is an exponential function. As x increases, the value of g(x) increases at an increasing rate.

Therefore, over the interval from x=8 to x=10, g(x) will increase at an increasing rate.

To see this, we can calculate g(8) and g(10) and observe the difference between the two values.

g(8) = 3^8 = 6561

g(10) = 3^10 = 59049

So, the rate is

Rate = 59049/6561

Rate = 9

This means that the rate is by a factor of 9

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After following all the listed steps, you can determine that it will be a graph with lines going through the y-int of -6.

The value of x in the given similar triangles is 30.8.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.

Given that the triangles are similar, thus the ratio of their sides are equal.

Here, 28/10 = x / 11

Using cross multiplication we have:

x = 28 / 10 (11)

x = 30.8

Hence, the value of x in the given similar triangles is 30.8.

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The final amount earned on the investment after 4 years is $900.40.

An investment of $800 is made at an annual interest rate of 3% compounded yearly for 4 years. To calculate the final amount earned on the investment after 4 years, we can use the formula for compound interest:

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

where:

A = the final amount

P = the principal investment, which is $800 in this case

r = the annual interest rate, which is 3% or 0.03 as a decimal

n = the number of times the interest is compounded per year, which is once per year in this case

t = the number of years, which is 4 in this case

Plugging in the values, we get:

A = 800(1 + 0.03/1)¹ˣ⁴

A = 800(1.03)⁴

A = 800(1.1255)

A = $900.40

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Answer:

linear

Step-by-step explanation:

yw